課程名稱Course Title (中文) 隨機過程 (英文) Random Variable & Stochastic Process 開課單位Departments 電機工程學系 課程代碼Course No. E4070 授課教師Instructor 龔宗鈞 學分數Credit 3.0 必/選修core required/optional 選修 開課年級Level 大四 先修科目或先備能力(Course Pre-requisites)：工程數學(微積分、矩陣、富氏分析) 課程概述與目標(Course Overview and Goals)：使學生了解隨機變數與隨機過程之數學理論與物理觀念，並能夠應用於系統上之分析與設計。 教科書(Textbook) 作者 : Peyton Z. Peebles, Jr. 書名 : Probability, Random Variables and Random Signal Principles 出版社 : McGraw Hill(ISBN 0-07-118181-4) 參考教材(Reference)
 課程大綱 Syllabus 學生學習目標Learning Objectives 單元學習活動Learning Activities 學習成效評量Evaluation 備註Notes 序No. 單元主題Unit topic 內容綱要Content summary 1 Introduction 1. Random variables 2. Random process To understand: the concept of random variables and random process. 講授 2 The Random Variable 1. The Random Variable Concept 2. Distribution Function 3. Density Function To understand: definition of random variable, conditions for a function to be a random variable, discrete and continuous random variable, mixed random variable, distribution function, density function. 講授 3 The Random Variable 1. The Gaussian Random Variable 2. Other Distribution and Density Examples 3. Conditional Distribution and Density Function To understand: definition of Gaussian random variable, other distribution and density examples, conditional distribution function, density function. 講授 作業 HW 1 4 Operations on One Random Variable (RV) 1. Expection 2. Moments To understand: expected value of a RV, expected value of a function of a RV, moments about the origin, central moments, variance and skew, Chebychev's inequality. 講授 5 Operations on One Random Variable (RV) 1. Transformations of a Random Variable To understand: monotonic transformations of a continuous RV, nonmonotonic transformations of a continuous RV, transformation of a discrete RV. 講授 作業 HW 2 6 Multiple Random Variables 1. Vector Random Variables 2. Joint Distribution and Its Properties 3. Conditional Distribution and Density To understand: joint distribution function and its properties, marginal distribution functions, conditional distribution and density. 講授 平時考 Quiz 1 7 Multiple Random Variables 1. Statistical Independence 2. Distribution and Density of a Sum of RVs 3. Central Limit Theorem To understand: statistical independence of RVs, distribution and density of a sum sum of two RVs, central limit theorem. 講授 8 期中考 筆試 課程複習及筆試 期中考 9 Operations on Multiple Random Variables 1. Expected Value of a Function of Random Variables 2. Joint Characteristic Functions 3. Joint Gaussian Random Variables To understand: joint moments about the origin, joint characteristic functions, joint Gaussian RVs. 講授 10 Random Processes-Temporal Characteristics 1. The Random Process Concept 2. Stationarity and Independence To understand: classification of processes, statistical independence, first-order stationary process, second-order and wide-sense stationarity, N-order and strict-sense stationarity, time average and ergodicity. 講授 11 Random Processes-Temporal Characteristics 1. Correlation Functions 2. Measurement of Correlation Functions To understand: autocorrelation function and its properties, cross-correlation function and its properties, covariance functions. 講授 作業 HW 3 12 Random Processes-Temporal Characteristics 1. Gaussian Random Processes 2. Poisson Random Processes To understand: the properties of Gaussian random processes, Poisson random processes 講授 平時考 Quiz 2 13 Random Processes-Spectral Characteristics Power Density Spectrum and Its Properties To understand: the power density spectrum and its properties, bandwidth of the power density spectrum. 講授 14 Random Processes-Spectral Characteristics Relationship between Power Spectrum and Autocorrelation Function To understand: relationship between power spectrum and autocorrelation function. 講授 作業 HW 4 15 Random Processes-Spectral Characteristics Cross-Power Density Spectrum and Its Properties To understand: the cross-power density spectrum and its properties. 演講 平時考 Quiz 3 16 期末考 筆試 課程複習及筆試 期末考 17 Linear Systems with Random Inputs 1. Linear System Fundamentals 2. Random Signal Response of Linear System To understand: mean and mean-squared value of system response, autocorrelation function of response, cross-correlation functions of input and output. 彈性教學 18 Linear Systems with Random Inputs Spectral Characteristics of System Response To understand: power density spectrums of response, cross-power density spectrums of input and output. 講授 彈性教學 HW 5 請於 2025/1/8 前於 Tronclass 繳交彈性教學週之作業HW5

 序No. 實施期間Period 實施方式Content 教學說明Teaching instructions 彈性教學評量方式Evaluation 備註Notes 1 起:2024-01-02 迄:2024-01-05 1.同步遠距教學 Synchronous distance learning 1. Linear System Fundamentals 2. Random Signal Response of Linear System 2 起:2024-01-08 迄:2024-01-12 1.同步遠距教學 Synchronous distance learning Spectral Characteristics of System Response 作業 請於 2024/1/12 前於 Tronclass 繳交彈性教學週之作業 HW 5

 教學要點概述： 1.自編教材 Handout by Instructor： □ 1-1.簡報 Slids □ 1-2.影音教材 Videos □ 1-3.教具 Teaching Aids ■ 1-4.教科書 Textbook ■ 1-5.其他 Other □ 2.自編評量工具/量表 Educational Assessment □ 3.教科書作者提供 Textbook 成績考核 Performance Evaluation： 期末考：30%   期中考：30%   彈性教學：10%   平時考：20%   作業：10%   教學資源(Teaching Resources)： ■ 教材電子檔(Soft Copy of the Handout or the Textbook) □ 課程網站(Website) 扣考規定：https://curri.ttu.edu.tw/p/412-1033-1254.php